Binary codes with locality for multiple erasures having short block length

This paper considers linear, binary codes having locality parameter r, that are capable of recovering from t ≥ 2 erasures and which additionally, possess short block length. Both sequential and parallel (through orthogonal parity checks) recovery are considered. In the case of sequential repair, the results include (a) extending and characterizing minimum-block-length constructions for t = 2, (b) providing improved bounds on block length for t = 3 as well as a general construction for t = 3 having short block length, (c) providing high-rate constructions for (r = 2, t ∈ {4, 5, 6, 7}) and (d) providing short-block-length constructions for general (r, t). In the case of parallel repair, minimum-block-length constructions are characterized whenever t|(r
²
+ r) and examples examined.